Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Iterative methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Convergence Analysis of the Alternating Anderson–Picard Method for Nonlinear Fixed-Point Problems

Anderson acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson–Picard (AAP) method. Furthermore, despite introducing more “slow” Picard iterations, this method has been shown to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear case. In this paper, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that uses GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP “converges” to the Newton-GMRES method. Specifically, as the residual approaches zero, the multisecant matrix, the approximate Jacobian inverse, the search direction, and the optimization gain of AAP converge to their counterparts in the Newton-GMRES method. These connections provide insights for analyzing the asymptotic convergence properties of AAP. Consequently, we show that AAP is locally 𝑞-linear convergent and provide an upper bound for the convergence factor of AAP. To validate the theoretical results, numerical examples are provided.

Anderson acceleration↗
DOE OSTI2014

An algorithm to estimate the object support in truncated images

Purpose: Truncation artifacts in CT occur if the object to be imaged extends past the scanner field of view (SFOV). These artifacts impede diagnosis and could possibly introduce errors in dose plans for radiation therapy. Several approaches exist for correcting truncation artifacts, but existing correction algorithms do not accurately recover the skin line (or support) of the patient, which is important in some dose planning methods. The purpose of this paper was to develop an iterative algorithm that recovers the support of the object. Methods: The authors assume that the truncated portion of the image is made up of soft tissue of uniform CT number and attempt to find a shape consistent with the measured data. Each known measurement in the sinogram is interpreted as an estimate of missing mass along a line. An initial estimate of the object support is generated by thresholding a reconstruction made using a previous truncation artifact correction algorithm (e.g., water cylinder extrapolation). This object support is iteratively deformed to reduce the inconsistency with the measured data. The missing data are estimated using this object support to complete the dataset. The method was tested on simulated and experimentally truncated CT data. Results: The proposed algorithm produces a better defined skin line than water cylinder extrapolation. On the experimental data, the RMS error of the skin line is reduced by about 60%. For moderately truncated images, some soft tissue contrast is retained near the SFOV. As the extent of truncation increases, the soft tissue contrast outside the SFOV becomes unusable although the skin line remains clearly defined, and in reformatted images it varies smoothly from slice to slice as expected. Conclusions: The support recovery algorithm provides a more accurate estimate of the patient outline than thresholded, basic water cylinder extrapolation, and may be preferred in some radiation therapy applications.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-C-304-01: Investigation of Various Detector Response Functions and Their Geometry Dependence in a Novel Method to Address Ion Chamber Volume Averaging Effect

Purpose: A novel convolution-based approach has been proposed to address ion chamber (IC) volume averaging effect (VAE) for the commissioning of commercial treatment planning systems (TPS). We investigate the use of various convolution kernels and its impact on the accuracy of beam models. Methods: Our approach simulates the VAE by iteratively convolving the calculated beam profiles with a detector response function (DRF) while optimizing the beam model. At convergence, the convolved profiles match the measured profiles, indicating the calculated profiles match the “true” beam profiles. To validate the approach, beam profiles of an Elekta LINAC were repeatedly collected with ICs of various volumes (CC04, CC13 and SNC 125) to obtain clinically acceptable beam models. The TPS-calculated profiles were convolved externally with the DRF of respective IC. The beam model parameters were reoptimized using Nelder-Mead method by forcing the convolved profiles to match the measured profiles. We evaluated three types of DRFs (Gaussian, Lorentzian, and parabolic) and the impact of kernel dependence on field geometry (depth and field size). The profiles calculated with beam models were compared with SNC EDGE diode-measured profiles. Results: The method was successfully implemented with Pinnacle Scripting and Matlab. The reoptimization converged in ∼10 minutes. For all tested ICs and DRFs, penumbra widths of the TPS-calculated profiles and diode-measured profiles were within 1.0 mm. Gaussian function had the best performance with mean penumbra width difference within 0.5 mm. The use of geometry dependent DRFs showed marginal improvement, reducing the penumbra width differences to less than 0.3 mm. Significant increase in IMRT QA passing rates was achieved with the optimized beam model. Conclusion: The proposed approach significantly improved the accuracy of the TPS beam model. Gaussian functions as the convolution kernel performed consistently better than Lorentzian and parabolic functions. Further improvement of using geometry-dependent kernels was marginal.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

QuadSync: Quadrifocal tensor synchronization via Tucker decomposition

In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge such beliefs by providing a new framework to recover n cameras from the corresponding collection of quadrifocal tensors. We form the block quadrifocal tensor and show that it admits a Tucker decomposition whose factor matrices are the stacked camera matrices, and which thus has a multilinear rank of (4,4,4,4) independent of n. We develop the first synchronization algorithm for quadrifocal tensors, using Tucker decomposition, alternating direction method of multipliers, and iteratively reweighted least squares. We further establish relationships between the block quadrifocal, trifocal, and bifocal tensors, and introduce an algorithm that jointly synchronizes these three entities. Numerical experiments demonstrate the effectiveness of our methods on modern datasets, indicating the potential and importance of using higher-order information in synchronization.

Miao, Daniel [University of Minnesota]↗
DOE OSTI2018

On Coarse Grid Correction Methods in Krylov Subspaces

Two approaches using coarse grid correction in the course of a certain Krylov iterative process are presented. The aim of the correction is to accelerate the iterations. These approaches are based on an approximation of the function sought for by simple basis functions having finite supports. Additional acceleration can be achieved if the iterative process is restarted and the approximate solution is refined. In this case, the resulting process turns out to be a two-level preconditioned method. The influence of different parameters of the iterative process on its convergence is demonstrated by numerical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: Tetrahedral molecules

A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB{sub 4} molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q){sup −2} type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH{sub 4} molecule is demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Implementation of Parallel Adaptive-Krylov Exponential Solvers for Stiff Problems

Recently exponential integrators have been receiving increased attention as a means of solving large stiff systems of ODEs. Preliminary performance analysis demonstrated that exponential integrators hold promise compared to state-of-the-art implicit methods. However, much work remains to be done to understand in detail possible computational advantages these methods may offer in practice. This is particularly true for supercomputer-scale problems as there has been very little work on parallelizing exponential methods. In this paper we describe an implementation of a suite of parallel exponential solvers. Additionally, we present some performance tests on four stiff benchmark problems of a particular adaptive-Krylov exponential propagation iterative Runge--Kutta (EPIRK) method from the suite, and compare efficiency with the Newton--Krylov implicit solver CVODE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Development of a Practical Secondary Control for Hardware Microgrids

Practical, vendor-agnostic interoperability guidelines for the secondary control architecture of microgrids (MGs) with multiple grid-forming (GFM) inverter-based resources (IBRs) have not yet been developed. Therefore, this paper proposes a generic and vendor-agnostic secondary control architecture that operates with all GFM IBRs and synchronous generators. This secondary control does not require the use of additional measurement devices in the MG and utilizes the inherent communication systems of the GFM units, such as Modbus TCP/IP. The practical challenges of Modbus registers, such as packet loss and quantization error, and their detrimental impacts on secondary control actions are investigated. The proposed three-stage modification for any secondary control architecture to mitigate these impacts includes: 1) averaging the data read, 2) situational event-triggering of the controller, and 3) finite iteration of the controlling action. The proposed method is validated using a 3-..phi.., 480 V, 60 Hz, 500 kVA laboratory hardware microgrid with commercial two GFM IBRs and one diesel generator. The experimental results corroborates the fact the proposed modification in the secondary control architecture is advantageous for practical usage under erroneous measurements.

communication systems↗
DOE OSTI2018

A novel low-rank matrix completion approach to estimate missing entries in Euclidean distance matrix

A Euclidean distance matrix (EDM) is a table of distance-square between points on a k-dimensional Euclidean space, with applications in many fields (e.g., engineering, geodesy, economics, genetics, biochemistry, and psychology). A problem that often arises is the absence (or uncertainty) of some EDM elements. In many situations, only a subset of all pairwise distances is available and it is desired to have some procedure to estimate the missing distances. In this paper, we address the problem of missing data in EDM through low-rank matrix completion techniques. We exploit the fact that the rank of a EDM is at most k+2 and does not depend on the number of points, which is, in general, much bigger then k. We use a singular value decomposition approach that considers the rank of the matrix to be completed and computes, in each iteration, a parameter that controls the convergence of the method. After performing a number of computational experiments, we could observe that our proposal was able to recover, with high precision, random EDMs with more than 1000 points and up to 98% of missing data in few minutes. In addition, our method required a smaller number of iterations when compared to other competitive state-of-art technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimization of battery swapping infrastructure for e-commerce drone delivery

Drone delivery is widely-researched to alter the current e-commerce delivery convention for providing short delivery lead times. Yet, flight range of drones, constrained by the available battery technology, sets a milestone toward realizing the sole-drone delivery. To tackle with the flight range limitation, locating automated battery swapping machines (ABSM) have been proposed and a few studies modeled the problem. Using the ABSMs, drones can be loaded with fully-charged batteries along the route to a demand location. Here, we introduce a mixed-integer nonlinear program to model the problem. The objective of the program is to optimally select ABSM locations, determine the delivery-mode choices (drone-only, truck-only, and mixed delivery) of demand locations, find drone delivery routes, and approximate the baseline requirements for the number of drones and batteries needed. The program minimizes the overall delivery system costs including: ABSM, delivery, drone ownership, battery inventory, and service congestion. A cutting-plane method is developed to find exact solutions in finite iterations. Computational experiments showed that the method quickly yields the optimal solution to instances with less than 60 ABSM candidates and 20 demand locations. A case study shows that the optimal drone delivery infrastructure can save almost 20% cost compared to the conventional truck-only delivery. Sensitivity analyses were conducted to reveal the impact of key parameters in the decision-making and found that a decrease in the ABSM and drone costs highly affect the system cost.

25 ENERGY STORAGE↗
DOE OSTI2020

A method for achieving complete microbial genomes and improving bins from metagenomics data

Metagenomics facilitates the study of the genetic information from uncultured microbes and complex microbial communities. Assembling complete microbial genomes ( i.e ., circular with no misassemblies) from metagenomics data is difficult because most samples have high organismal complexity and strain diversity. Less than 100 circularized bacterial and archaeal genomes have been assembled from metagenomics data despite the thousands of datasets that are available. Circularized genomes are important for (1) building a reference collection as scaffolds for future assemblies, (2) providing complete gene content of a genome, (3) confirming little or no contamination of a genome, (4) studying the genomic context and synteny of genes, and (5) linking protein coding genes to ribosomal RNA genes to aid metabolic inference in 16S rRNA gene sequencing studies. We developed a method to achieve circularized genomes using iterative assembly, binning, and read mapping. In addition, this method exposes potential misassemblies from k-mer based assemblies. We chose species of the Candidate Phyla Radiation (CPR) to focus our initial efforts because they have small genomes and are only known to have one ribosomal RNA operon. We present 34 circular CPR genomes, one circular Margulisbacteria genome, and two circular megaphage genomes from 19 public and published datasets. We demonstrate findings that would likely be difficult without circularizing genomes, including that ribosomal genes are likely not operonic in the majority of CPR, and that some CPR harbor diverged forms of RNase P RNA. Code and a tutorial for this method is available at https://github.com/lmlui/Jorg .

Lui, Lauren↗
DOE OSTI2024

Handling Iterative Solvers in an Algorithmic Differentiation Framework Using Implicit Methods

Differentiable programming is a powerful concept as it enables the seemly propagation of gradients through functions, algorithms, and/or whole physics simulations. These gradients are useful for a wide variety of applications, including sensitivity studies and machine learning, but one of particular interest is optimization. Gradient-based optimization, enabled through automatic/algorithmic differentiation (AD), can be used on predictive physical models to efficiently optimize a set of design variables. AD methods are a particularly promising approach to complex physics simulations because they can be shown to scale well with an increasing number of design variables; however, care must be taken when coupling between different models or different states of a single model.

algorithmic differentiation↗
DOE OSTI2014

Fast optimization of binary clusters using a novel dynamic lattice searching method

Global optimization of binary clusters has been a difficult task despite of much effort and many efficient methods. Directing toward two types of elements (i.e., homotop problem) in binary clusters, two classes of virtual dynamic lattices are constructed and a modified dynamic lattice searching (DLS) method, i.e., binary DLS (BDLS) method, is developed. However, it was found that the BDLS can only be utilized for the optimization of binary clusters with small sizes because homotop problem is hard to be solved without atomic exchange operation. Therefore, the iterated local search (ILS) method is adopted to solve homotop problem and an efficient method based on the BDLS method and ILS, named as BDLS-ILS, is presented for global optimization of binary clusters. In order to assess the efficiency of the proposed method, binary Lennard-Jones clusters with up to 100 atoms are investigated. Results show that the method is proved to be efficient. Furthermore, the BDLS-ILS method is also adopted to study the geometrical structures of (AuPd){sub 79} clusters with DFT-fit parameters of Gupta potential.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Narrowing the gap between the promise and reality of polyketide synthases as a synthetic biology platform

Engineering modular polyketide synthases (PKSs) has the potential to be an effective methodology to produce existing and novel chemicals. However, this potential has only just begun to be realized. We propose the adoption of an iterative design-build-test-learn paradigm to improve PKS engineering. We suggest methods to improve engineered PKS design by learning from laboratory-based selection; adoption of DNA design software and automation to build constructs and libraries more easily; tools for the expression of engineered proteins in a variety of heterologous hosts; and mass spectrometry-based high-throughput screening methods. Finally, lessons learned during iterations of the design-build-test-learn cycle can serve as a knowledge base for the development of a single retrosynthesis algorithm usable by both PKS experts and non-experts alike.

Poust, S↗
DOE OSTI2015

A point implicit time integration technique for slow transient flow problems

We introduce a point implicit time integration technique for slow transient flow problems. The method treats the solution variables of interest (that can be located at cell centers, cell edges, or cell nodes) implicitly and the rest of the information related to same or other variables are handled explicitly. The method does not require implicit iteration; instead it time advances the solutions in a similar spirit to explicit methods, except it involves a few additional function(s) evaluation steps. Moreover, the method is unconditionally stable, as a fully implicit method would be. This new approach exhibits the simplicity of implementation of explicit methods and the stability of implicit methods. It is specifically designed for slow transient flow problems of long duration wherein one would like to perform time integrations with very large time steps. Because the method can be time inaccurate for fast transient problems, particularly with larger time steps, an appropriate solution strategy for a problem that evolves from a fast to a slow transient would be to integrate the fast transient with an explicit or semi-implicit technique and then switch to this point implicit method as soon as the time variation slows sufficiently. We have solved several test problems that result from scalar or systems of flow equations. Our findings indicate the new method can integrate slow transient problems very efficiently; and its implementation is very robust.

42 ENGINEERING↗
DOE OSTI2024

All-optical image denoising using a diffractive visual processor

Abstract Image denoising, one of the essential inverse problems, targets to remove noise/artifacts from input images. In general, digital image denoising algorithms, executed on computers, present latency due to several iterations implemented in, e.g., graphics processing units (GPUs). While deep learning-enabled methods can operate non-iteratively, they also introduce latency and impose a significant computational burden, leading to increased power consumption. Here, we introduce an analog diffractive image denoiser to all-optically and non-iteratively clean various forms of noise and artifacts from input images – implemented at the speed of light propagation within a thin diffractive visual processor that axially spans <250 × λ, where λ is the wavelength of light. This all-optical image denoiser comprises passive transmissive layers optimized using deep learning to physically scatter the optical modes that represent various noise features, causing them to miss the output image Field-of-View (FoV) while retaining the object features of interest. Our results show that these diffractive denoisers can efficiently remove salt and pepper noise and image rendering-related spatial artifacts from input phase or intensity images while achieving an output power efficiency of ~30–40%. We experimentally demonstrated the effectiveness of this analog denoiser architecture using a 3D-printed diffractive visual processor operating at the terahertz spectrum. Owing to their speed, power-efficiency, and minimal computational overhead, all-optical diffractive denoisers can be transformative for various image display and projection systems, including, e.g., holographic displays.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A calibration method for overconstrained spatial translational parallel manipulators

A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90% are achievable.

42 ENGINEERING↗